For 1.13, the current version is 1.3.4 for Wesnoth 1.13.12 and up.
For 1.12, the current version is 1.2.2 for Wesnoth 1.11/12. Wesnoth 1.11.15 or greater is required.

Description for Wesnoth 1.13
Select an era, choose your faction, and lead it to victory against random factions over a series of random maps.
(Intermediate level, 7 scenarios.)

Any Default or Age of Heroes style era can be selected. If an Age of Heroes style era is selected, the campaign will start at scenario 4. It's recommended to use normal eras (i.e. eras that are just collections of factions). If the era contains events or other game play mechanics, unexpected results or incompatibilities may occur.

Modifications may or may not work with this add-on, use at own risk. However, the Custom Campaign modification is guaranteed to work.

Requires the latest versions of 'Era of Legends' & 'Ultimate Random Maps' to be installed.

Description for Wesnoth 1.12

Spoiler:

A one player multiplayer campaign.
Select an era, choose your faction, and lead it to victory against random factions over a series of random maps. For the standard experience, choose the Random Campaign Default era.
(Intermediate level, 7 scenarios.)

The campaign is balanced for being played with 'use map settings', though any setting on the Configure Game screen can be changed, and will take effect throughout the campaign.

The following unit advancement defines are enabled in this campaign: Ancient Lich, Armageddon Drake, Dwarvish Arcanister, & Orcish High Warlord.

Any Default or Age of Heroes style era can be selected. If an Age of Heroes style era is selected, the campaign will start at scenario 4. It's recommended to use normal eras (i.e. eras that are just collections of factions). If the era contains events or other game play mechanics, unexpected results or incompatibilities may occur.

Modifications may or may not work with this add-on, use at own risk. However, there is special cross-functionality with Custom Campaign. Upon finishing Random Campaign, your army will be saved for use in Custom Campaign, even if you don't have it. If the Custom Campaign modification is used when starting Random Campaign, it will allow you to select one of your armies for the campaign.

Requires BfW 1.11.15 or greater. Requires the latest versions of 'Era of Legends' & 'Ultimate Random Maps' to be installed.

Description for Wesnoth 1.10

Spoiler:

Play a random campaign with the faction of your choice.
In the Campaign section, play a 7 scenario campaign with factions from the default era.
In the Multiplayer section choose your era and faction, then pick between two versions, a 4 scenario campaign for 1 player, or a version for up to 3 players.
9 possible random map types ensure battles in a wide variety of situations.
Each battle is against one opponent, encouraging the application of sound basic strategy combined with faction specific adjustments.
Requires Sigurd's Random Maps, Era of Legends, Default+Khalifate Era, and Age of Heroes+Khalifate Era add-ons.

Old first post:

Spoiler:

The current version works 1.9.9 Wesnoth

Intent of Campaign:
Allow the player to play the faction of choice in a campaign setting, giving the experience of building, maintaining, & fighting with an army of the chosen faction over mulitple scenarios, in varying situations.

Current version 0.8.0a
Features:
Play a random campaign with the era and faction of your choice, including any you have downloaded! In the Campaign section, play a 6 scenario campaign using factions from the default era. In the Multiplayer section choose your era and faction, then pick between two versions, a 3 scenario campaign for 1 player, or a version for up to 3 players. 11 possible random map types ensure battles in a wide variety of situations.

Normal difficulty has been been tested, easy & hard have not.Currently throws up a Invalid WML regarding my use of the [generator] tag, but it's working anyway. 1.9.5 seems to have fixed it

You jump from scenario 1 straight to 3.
Maybe it would have been possible to create a story too ?
"Invalid WML found: [generator] not supported at scenario toplevel" may be a bug I think (it IS supported).

I do plan on adding story, but as my code stands, I'm gonna have to rewrite the first scenario to be a faction selection only, then to advance to the proper map, presenting the story there. Unless anyone has an idea on how I can make my faction selection menu occur before story (for the first map. subsequent maps don't have that problem.

EDIT - Took less time than I thought it would to rewrite first scenario into a faction selection only

As there is a lot of variety amongst the maps, the turn limit has been removed
Bonus gold (which wasn't being used) was removed
Difficulty levels are now Clear, Fog, Shroud.
Clear uses the previous Easy gold schedule, Fog & Shroud use the previous Normal gold schedule.
Most of the code was cleaned up extensively.
The map generators have just about everything in them macro'ed for easy readability
Faction data is now read directly from the mainline multiplayer/factions/ files.
This makes future updating easier & also makes it easier for knowledgeable users to edit Faction_Data.cfg file in the campagin to load their own factions/eras

The random map generators have been made avaiable as a seperate Multiplayer Map Pack on the add-on server as "RC Map Pack"

I'm going to take a break from working on this for at least a month. Comments are still wanted & will be read during that time

Changes
Only for Wesnoth 1.9.5, as new terrain has been added to the maps (sand drifts & water lilies)
Added new random map type, Island.
Added a 1 player, 3 scenario campaign under multiplayer, allowing use of most Eras! & configuration of most settings.
Various tweaks to most of the random maps.
Changed name of time on Citadel from Indoors to Citadel.
Added code to insure than no map is repeated during a campaign.

RC Map Pack has been updated as well.

Future version possibities:
Removal of SP AOH 3 scenario, as it is made redundant by the MP side 3 scenario campaign.
Change of difficulty levels back to Easy,Normal,Hard with gold settings to match, & likely with fog,shroud,shroud.
Making the 6 scenario SP campaign more in line with what is typically done with a campaign.
As I'm running out of gameplay features/changes, might finally get around to improved dialogue & adding story.
Clean up SP code, it seems rather messy & unnecessarly complex.
Maybe some other stuff, once I sit down and do some thinking about design & direction for this campaign.

Works with 1.9.5 & 1.9.6 Wesnoth
Added a true multiplayer campaign for up to 3 players. Can be configured
same way as the 1 player MP Campaign. If there are OOS errors or other bugs in
the 3 player version, please post in the forums, as I have no way of testing for OOS errors myself.
Added more random dialogue.
Added some story.
Removed 3 scenario campaign on the SP Campagin side as it's redundant.
Removed 'Random' faction choice on SP Campaign, as there's no good reason to pick it,
when you could get stuck with a leader that maxes out at level 2 for the whole campaign.
Changed names of SP difficulty back to EASY, NORMAL, HARD; with appropriate gold values.
Fog is present on all levels, shroud set to no,yes,yes for difficulty.

Future possibilies:
Map tweaking
Random items
Clean up code
Expand dialogue
Adding Khalifate to the 6 scenario version when the bugs are worked out.

Just a tip:
In the description of your campain on the addons server you say that you have no way to test fro OOS errors. That's probably wrong. Start two instances of BfW and connect with both of them to the server to play in mp with your (the other instance's) self. No need for 2 PCs. And use :inspect to inspect the gamestate if there are OOS.

Works with 1.9.9 or greater.
Khalifate added to the 6 Scenario Campaign.
Map generators have been exported to Sigurd's Random Maps, which is now a required dependency.
Upon completion of Campagin or 1p Multiplayer version, you have the choice to save your army for use in Custom Campaign, even if you don't have it yet.
Other minor tweaks and some code cleanup.

Edit: Version 0.8.3e is up. (11-13-2011)
Removes Khalifate (they will be readded when an add-on for them has been released.)
Removes Save to Custom Campaign feature, which became broken with Custom Campaign 0.9.0. May eventually be added back in.

The purpose of RC has always been:
A way to play a faction in a campaign setting, and be able to level up units and apply different strategies & tactics to random opponents on random maps.

The following sums up the changes I'm implementing to better carry out the purpose.

1. More traditonal campaign elements. (ie, turn limit, a little bit of bonus gold, etc)
2. Scenarios that are more focused to faction vs faction strategy.
3. A campaign that would rate as Intermediate difficulty.

As such, the charlie foxtrot of scenarios vs 1 then 2 then 3 opponents is being scraped. All scenarios will be against a single opponent to bring out more of the faction vs faction strategy & tactics. To be conducive to a turn limit, it's likely that Cave and Citadel will be removed from the map pool. Map sizes will be set to 30x30 across all scenarios. (I don't see much of a benefit in different sizes.)

The SP Campaign will be 7 scenarios, and each of the 7 factions will be used once (Khalifate included). Difficultly will be changed back to Clear, Fog, Shroud; with each having the same gold allotment. The first 3 scenarios will be using Default level, the next 3 using AoH, and the last using EoL (Era of Legends). The upgrading of the recruit list will now occur at the end of scenario 6. Most of the Extra_defines are being enabled, so each faction will have at least one unit type that can be leveled to level 4.

The MP 1p Campaign will still be 3 scenarios, but versus only one opponent each scenario, and will have code to reduce chances of playing the same faction twice. There will be "use map settings" for a recommended configuration that will match the first 3 levels of the SP version as much as possible, set on fog. This version will still work with any era. (At least ones that are just sets of factions, anything with gameplay changes may or may not work.)

The MP 3p Campaign may or may not be scrapped. Does anyone play this? I'm not into mp at all, I haven't even played it. If I keep it, it will have it's interface changed to be in line with the MP 1p version, but with appropriate changes to accomadate 2-3 players.

Add-on wide changes:
Random Campaign now requires the following add-ons:
Sigurd’s Random Maps, Era of Legends, Default + Khalifate Era, & Age of Heroes + Khalifate Era
Turn limit of 30 turns for each scenario except the last, which is unlimited.
All random maps used are 30x30 in size.
All campaigns have experience modifier of 100%.
Random map list has been reduced to accommodate turn limit better.
Maps are: Barren,Desert,Flood,Jungle,Marsh,River,Vale,Volcano,Winter
Each scenario is now against one opponent to bring out faction vs. faction play.
All leaders (player & enemy) get the ‘heroic’ trait. (props to WC & TGQ for inspiration.)
Additional dialog and changes to insure that dialog does not repeat during the campaign.

SP campaign specific changes:
7 scenarios.
Enemy factions do not repeat throughout campaign.
The first 3 enemies will be Default level, the next 3 AoH, and the last EoL.
4 difficulty levels in SP. They are the standard Easy, Normal, Hard, & Nightmare.
Normal should be balanced where I want it to be, the others may need some adjustment.
Visibility setting (Clear, Fog, Shroud) is a choice independent of difficulty level.
Default difficulty is ‘Normal’ and rates as intermediate in difficulty.
Dwarvish Runesmith has been added to the choices for leader for Knalgan Alliance.
Extra defines used to allow leveling to an Ancient Lich, Armageddon Drake, Dwarvish Arcanister, and Orcish High Warlord (an EoL unit) so that you can get a level 4 unit over the course of the campaign for any faction chosen.
Random options are now in the start menu, and match the mp faction/leader/gender selection as much as possible.
Use of gender symbols & unit images in gender selection in start menu.
The upgrading of the recruit list to AoH strength now occurs at the end of scenario 6.
Upon completion of campaign there is the option to save your army for use in Custom Campaign.

MP 1p campaign specific changes:
Game creation text map replaced with map that looks like the random unit dice icon. (white in color.)
‘Use default settings’ is equivalent to SP campaign ‘Normal’
4 scenarios, with the last being against a large swarm of enemy troops, to end with a challenge.
Enemy factions are unlikely to repeat over the course of the campaign.
Upon completion of campaign there is the option to save your army for use in Custom Campaign.

MP 3p campaign specific changes:
Game creation text map replaced with map that looks like the random unit dice icon. (tan in color.)
Default village gold of 2
Enemy factions are unlikely to repeat over the course of the campaign.

Misc:
No bonus gold, with the variableness in village placement & village numbers it’s just not practical.

This marks the start of the final phase of work on Random Campaign for the 1.10 branch. There might be some minor changes before the 1.0.0 version is released, though it’s my intention for the campaign to remain as it is now.